The speed v (in mer per second) of a falling object from rest, given the height h in meter can be calculated.

v^2 = u^2+2gh, wher u is the initial velocity V is the final velocity when a falling distance is h. g is the acceleration due to gravity.

A)

To find the speed when the diver is above 5.8m from water.

h = initial heiht of the diver - 5.8m = 4.8m, u=0

V^2 = U^2+2gh =0+2*9.81*4.8

v=sqrt(2*9.81*4.8) = 9.7044m/s

B)

The speed of the diver just before touching the water surface v = sqrt(2*9.81*9m), as here h=9 meter.

=13.2883 m/s.

C)

The initial speed is upward and so u = 2.9m/s as direction of moving towards water is assumed positive. This could be solved by using equation of motion for the vertically upward projected . But the magnitude of the speed remains same 2.9m/s while crossing the board in downward direction.Threfre,